Moderate -0.8 This is a straightforward work-energy question requiring only the formula W = Fs cos θ, where students must identify the horizontal component of tension (5 cos 30°) and multiply by distance traveled (0.4 × 10 = 4m). It's simpler than average A-level mechanics as it involves direct application of a single formula with no problem-solving or multi-step reasoning required.
1
\includegraphics[max width=\textwidth, alt={}, center]{430f1f9a-7a3a-47a0-b742-daf74e68adfd-2_300_748_274_708}
One end of a light inextensible string is attached to a ring which is threaded on a fixed horizontal bar. The string is used to pull the ring along the bar at a constant speed of \(0.4 \mathrm {~ms} ^ { - 1 }\). The string makes a constant angle of \(30 ^ { \circ }\) with the bar and the tension in the string is 5 N (see diagram). Find the work done by the tension in 10 s .
For using \(WD = Fd\cos\alpha\) or \(P = Fv\cos\alpha\) and \(WD = Pt\)
M1
Their distance; cos or sin but not just \(5\times4\)
\(WD = 5(0.4 \times 10)\cos 30°\)
A1
Radians M1 A1 A0 (max 2 out of 3); answer 3.085 does not score final A mark but may imply previous A1
Work done is \(17.3\) J (or \(10\sqrt{3}\))
A1
SR: Power is \(1.73\) W (max 1 out of 3)
B1
For candidates who calculate power only
# Question 1:
| Answer/Working | Mark | Guidance |
|---|---|---|
| For using $WD = Fd\cos\alpha$ or $P = Fv\cos\alpha$ and $WD = Pt$ | M1 | Their distance; cos or sin but not just $5\times4$ |
| $WD = 5(0.4 \times 10)\cos 30°$ | A1 | Radians M1 A1 A0 (max 2 out of 3); answer 3.085 does not score final A mark but may imply previous A1 |
| Work done is $17.3$ J (or $10\sqrt{3}$) | A1 | |
| SR: Power is $1.73$ W (max 1 out of 3) | B1 | For candidates who calculate power only |
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\includegraphics[max width=\textwidth, alt={}, center]{430f1f9a-7a3a-47a0-b742-daf74e68adfd-2_300_748_274_708}
One end of a light inextensible string is attached to a ring which is threaded on a fixed horizontal bar. The string is used to pull the ring along the bar at a constant speed of $0.4 \mathrm {~ms} ^ { - 1 }$. The string makes a constant angle of $30 ^ { \circ }$ with the bar and the tension in the string is 5 N (see diagram). Find the work done by the tension in 10 s .
\hfill \mbox{\textit{CAIE M1 2002 Q1 [3]}}